Related papers: Complexity invariance by replication in the quantu…
The diverse range of resources which underlie the utility of quantum states in practical tasks motivates the development of universally applicable methods to measure and compare resources of different types. However, many of such approaches…
We shed new light on entanglement measures in multipartite quantum systems by taking a computational-complexity approach toward quantifying quantum entanglement with two familiar notions--approximability and distinguishability. Built upon…
Quantum Hamilton-Jacobi quantization scheme uses the singularity structure of the potential of a quantum mechanical system to generate its eigenspectrum and eigenfunctions, and its efficacy has been demonstrated for several well known…
This paper shows that the concept of complex frequency, originally introduced to characterize the dynamics of signals with complex values, constitutes a generalization of eigenvalues when applied to the states of linear time-invariant (LTI)…
In our thesis, we try to shed more light onto the complexity of quantum complexity classes by refining the related part of the hierarchy. First, we review the basic concepts of quantum computing in general. Then, inspired by BQP, we define…
A field of random space-time events exhibiting complete spatial-temporal randomness appears statistically identical to all observers. Boost invariant lengths naturally emerge when we examine fluctuation scales of this field such as the…
We show a continuity result for the Weyl pseudometric on subshifts which are generated by model sets. This fact is then used for multiple constructions of subshifts that exhibit different behavior regarding entropy, amorphic complexity and…
A measure of complexity based on a probabilistic description of physical systems is proposed. This measure incorporates the main features of the intuitive notion of such a magnitude. It can be applied to many physical situations and to…
The distribution of coherence in multipartite systems is one of the fundamental problems in the resource theory of coherence. To quantify the coherence in multipartite systems more precisely, we introduce new coherence measures,…
Realistic quantum mechanics based on complex probability theory is shown to have a frequency interpretation, to coexist with Bell's theorem, to be linear, to include wavefunctions which are expansions in eigenfunctions of Hermitian…
Quantum coherence is the key resource for quantum technology, with applications in quantum optics, information processing, metrology and cryptography. Yet, there is no universally efficient method for quantifying coherence either in…
Quantum mechanical potentials satisfying the property of shape invariance are well known to be algebraically solvable. Using a scaling ansatz for the change of parameters, we obtain a large class of new shape invariant potentials which are…
We demonstrate that certain class of infinite sums can be calculated analytically starting from a specific quantum mechanical problem and using principles of quantum mechanics. For simplicity we illustrate the method by exploring the…
Complex numbers are widely used in both classical and quantum physics, and play an important role in describing quantum systems and their dynamical behavior. In this paper we study several measures of imaginarity of quantum states in the…
Coherence and entanglement are fundamental properties of quantum systems, promising to power the near future quantum computers, sensors and simulators. Yet, their experimental detection is challenging, usually requiring full reconstruction…
We consider universal aspects of two problems: (i) the slow purification of a large number of qubits by repeated quantum measurements, and (ii) the singular value structure of a product ${m_t m_{t-1}\ldots m_1}$ of many large random…
Gaussian Klauder coherent states are discussed in the context of the infinite well quantum model, otherwise known as the particle in a box. A supersymmetric partner system is also presented, as well as a construction of coherent states in…
The usual conjectures of quantum measurements approaches, inspired from the traditional interpretation of Heisenberg's ("uncertainty") relations, are proved as being incorrect. A group of reconsidered conjectures and a corresponding new…
We use entropy to link fine-structure constant and cosmological constant. We also link nuclear force and gravity. We step on the fundamentals of consciousness for this new millennium with a scientific approach. Statistical and quantum…
The concept of quantum complexity has far-reaching implications spanning theoretical computer science, quantum many-body physics, and high energy physics. The quantum complexity of a unitary transformation or quantum state is defined as the…